A 34.0 kg child slides down a long slide in a playground. She starts from rest at a height h1 of 23.00 m. When she is partway down the slide, at a height h2 of 13.00 m, she is moving at a speed of 7.50 m/s. Calculate the mechanical energy lost due to friction (as heat, etc.).

Conservation of energy says:

PE + KE + energy lost to friction = 0.

PE is equal to mgh and is a negative number as the child moves downhill. The change in KE is 1/2mv^2. So now you have everything you need to calculate the energy lost to friction. Post back with your answer and we'll check it for you.